Calculate the Area: Finding Ascending Region of f(x)=6x²-12

To determine the ascending area of the function $f(x) = 6x^2 - 12$, we will follow these steps:

• Step 1: Calculate the derivative of the given function.
• Step 2: Set the inequality $f'(x) > 0$ to find the interval where the function is increasing.
• Step 3: Solve the inequality for $x$.

Let's begin with Step 1:
The derivative of $f(x) = 6x^2 - 12$ with respect to $x$ is:

$f'(x) = \frac{d}{dx}(6x^2 - 12) = 12x$.

Step 2: We need to find where $12x > 0$. This requires:

$x > 0$.

Step 3: Therefore, the function $f(x) = 6x^2 - 12$ is increasing when $x > 0$.

Thus, the increasing interval of the function is when $x > 0$.

The solution to the problem is $0 < x$.